Depth of Field on glossy surfaces (cycles)
If the reflective ball is inside the FOV, it will probably still preserve the sharp image due to light path has been concentrate from outer light, it will be harder to tell the blur effect if a convex mirror is presented.

And also, they do have a Depth of Field reflection, if you turn down the F-Stop to extremely small,  and using a giant sensor that have ever been made in camera history. You should see the blur inside the Convex mirror

 You can notice that the little tiny Susanne is clear while the whole mirror even around the tiny Susanne is blur, due to the natural light path.

What you encounter is because normally, we don't have this kind of lens, way too impossible to make it perfectly. If we only get the ordinary lens with a long focus len (125mm) and big enough Aperture (F/2.8 or something). The depth of field should be narrow enough to see the blur effect in object easily. But that only occur in diffuse object not the convex reflective.

Assume that your reflective scene is in far far away (like an HDR environment map or sky). You should get the maximal blur effect right? See the figure below with a normal lens:



"Hey, the light path change a lot of angle. Reflective should be blur as well". Unfortunately, Blender didn't show the real effective aperture size in camera icon. So I made one for it:



See that ridiculous tiny circle in front of camera? That is the real effective aperture size in Blender default 1 meter as 1 unit. So it is almost a dot for that reflective mirror if you put it in a distance. And follow up the light path you should see clear image unless you properly setup the scene size.